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15 June 2015 Faber–Krahn inequalities in sharp quantitative form
Lorenzo Brasco, Guido De Philippis, Bozhidar Velichkov
Duke Math. J. 164(9): 1777-1831 (15 June 2015). DOI: 10.1215/00127094-3120167

Abstract

The classical Faber–Krahn inequality asserts that balls (uniquely) minimize the first eigenvalue of the Dirichlet Laplacian among sets with given volume. In this article we prove a sharp quantitative enhancement of this result, thus confirming a conjecture by Nadirashvili and by Bhattacharya and Weitsman. More generally, the result applies to every optimal Poincaré–Sobolev constant for the embeddings W 0 1 , 2 ( Ω ) L q ( Ω ) .

Citation

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Lorenzo Brasco. Guido De Philippis. Bozhidar Velichkov. "Faber–Krahn inequalities in sharp quantitative form." Duke Math. J. 164 (9) 1777 - 1831, 15 June 2015. https://doi.org/10.1215/00127094-3120167

Information

Received: 14 June 2013; Revised: 21 September 2014; Published: 15 June 2015
First available in Project Euclid: 15 June 2015

zbMATH: 1334.49149
MathSciNet: MR3357184
Digital Object Identifier: 10.1215/00127094-3120167

Subjects:
Primary: 47A75
Secondary: 49Q20, 49R05

Rights: Copyright © 2015 Duke University Press

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Vol.164 • No. 9 • 15 June 2015
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